Arithmetical geometry and number theory - A conference in honor of N. Katz

主要研究人员：Brian ConreyProposal Number：DMS-0306938机构：美国算术几何和数论学会，纪念N.M.Katz的会议摘要：在Weil，Grothendieck和Deligne的工作之后，有限域上变元的Zeta函数理论已经成为数论和几何中非常强大的工具。Katz一直是并将继续是这些领域的领先研究人员，并一直支持它们的应用。他的贡献范围从指数和、单数群及其表示、数论、模形式经典和p-进，到算术模问题。所有这些领域在很大程度上仍处于当前研究的中心。PIS将就这些相互关联的领域举行为期4天的会议。时间与卡茨60岁生日不谋而合。这次会议将汇集这些领域的许多顶尖研究人员，就最新发展发表演讲。除了这些高级讲座外，会议还将为研究生和博士后提供调查讲座和讨论课程。数论和算术几何数学领域的结合部分涉及代数方程(如费马方程)的计数解的研究，其中解是整数。对这些问题的研究需要一些最复杂的现代数学理论。掌握和发展这些理论的回报是巨大的。例如，在纯数学的其他领域，以及应用离散数学的领域，如计算机科学、最佳效率网络的设计和密码学，都有深远的应用。这次为期4天的会议将以这一重要的数学为特色，特别是那些与N.M.Katz最感兴趣的方面，他是这些领域的世界领导者。将特别注意将研究生和博士后助理纳入会议的所有方面。调查讲座和对年轻数学家特别有用的正式讨论会议将是会议的一个亮点。

Principal Investigator: Brian ConreyProposal Number: DMS -0306938Institution: American Institute of Mathematics Arithmetical geometry and number theory, a conference in honor of N. M. KatzAbstract:After the works of Weil, Grothendieck, and Deligne, the theory of zeta functions of varieties over finite fields has been a very powerful tool in number theory and geometry. Katz has been and continues to be a leading researcher in these areasand has championed their applications. His contributions range from exponential sums, monodromy groups and their representations, number theory, modular forms classical and p-adic, to arithmetic moduli problems. All of these areas are still very much at the center of current research. The PIs will conduct a 4 day conference on these connected areas. The timing will coincide with Katz' 60 th birthday. The conference will bring together many of the leading researchers in these fields to lecture on the latest developments. In addition to these advanced lectures the conference will also feature survey lectures and discussion sessions aimed forgraduate students and postdocs.The combination of the mathematical fields of number theory and arithmetical geometry is concerned in part with the study of counting solutions to algebraic equations (such as Fermat's equation) where the solutions are to be whole numbers. The study of such problems requires some of the most sophisticated modern mathematical theories. The payoff for mastering and developing these theories is great. For instance, there are far-reaching applications to other areas of pure mathematics as well as to areas of applied discrete mathematics such as computer science, to the design of optimally efficient networks and to cryptography. This 4-day conference will feature this important mathematics, especially those aspects closest to the interests of N. M. Katz who is a world leader in these areas. Particular attention will be devoted to including graduate students and postdoctoral associates in all aspects of the conference. Survey lectures and formal discussion sessions which will be particularly useful to younger mathematicians will be a highlight of the conference.